A055844 a(n) = (5*n + 9)*binomial(n+8, 8)/9.

1, 14, 95, 440, 1595, 4862, 13013, 31460, 70070, 145860, 286858, 537472, 965770, 1673140, 2806870, 4576264, 7272991, 11296450, 17185025, 25654200, 37642605, 54367170, 77388675, 108689100, 150762300, 206719656, 280412484, 376573120

Offset: 0

Author

Barry E. Williams, May 30 2000

Keywords

• easy
• nonn

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A052255.

Cf. A093562 ((5, 1) Pascal, column m=9).

Programs

GAP

List([0..30], n-> (5*n+9)*Binomial(n+8, 8)/9); # G. C. Greubel, Jan 21 2020

Magma

[(5*n+9)*Binomial(n+8, 8)/9: n in [0..30]]; // G. C. Greubel, Jan 21 2020

Maple

seq((5*n+9)*binomial(n+8, 8)/9, n=0..30); # G. C. Greubel, Jan 21 2020

Mathematica

Table[5*Binomial[n+9,9] -4*Binomial[n+8,8], {n,0,30}] (* G. C. Greubel, Jan 21 2020 *)

PARI

vector(31, n, (5*n+4)*binomial(n+7, 8)/9) \\ G. C. Greubel, Jan 21 2020

Sage

[(5*n+9)*binomial(n+8, 8)/9 for n in (0..30)] # G. C. Greubel, Jan 21 2020

Formula

a(n) = (5*n+9)*binomial(n+8, 8)/9.

G.f.: (1+4*x)/(1-x)^10.

From G. C. Greubel, Jan 21 2020: (Start)

a(n) = 5*binomial(n+9, 9) - 4*binomial(n+8, 8).

E.g.f.: (362880 +4717440*x [phone]*x^2 [phone]*x^3 +5292000*x^4 +1227744*x^5 +155232*x^6 +10656*x^7 +369*x^8 +5*x^9)*exp(x)/362880. (End)